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Quadratic Binary Programming and Dynamical System Approach to Determine the Predictability of Epileptic Seizures

Author

Listed:
  • L.D. Iasemidis

    (Arizona State University)

  • P. Pardalos

    (University of Florida)

  • J.C. Sackellares

    (University of Florida)

  • D.-S. Shiau

    (University of Florida)

Abstract

Epilepsy is one of the most common disorders of the nervous system. The progressive entrainment between an epileptogenic focus and normal brain areas results to transitions of the brain from chaotic to less chaotic spatiotemporal states, the epileptic seizures. The entrainment between two brain sites can be quantified by the T-index from the measures of chaos (e.g., Lyapunov exponents) of the electrical activity (EEG) of the brain. By applying the optimization theory, in particular quadratic zero-one programming, we were able to select the most entrained brain sites 10 minutes before seizures and subsequently follow their entrainment over 2 hours before seizures. In five patients with 3–24 seizures, we found that over 90% of the seizures are predictable by the optimal selection of electrode sites. This procedure, which is applied to epilepsy research for the first time, shows the possibility of prediction of epileptic seizures well in advance (19.8 to 42.9 minutes) of their occurrence.

Suggested Citation

  • L.D. Iasemidis & P. Pardalos & J.C. Sackellares & D.-S. Shiau, 2001. "Quadratic Binary Programming and Dynamical System Approach to Determine the Predictability of Epileptic Seizures," Journal of Combinatorial Optimization, Springer, vol. 5(1), pages 9-26, March.
    • Handle: RePEc:spr:jcomop:v:5:y:2001:i:1:d:10.1023_a:1009877331765
    DOI: 10.1023/A:1009877331765
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    Citations

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    Cited by:

    1. Wei Chen & Liansheng Zhang, 2010. "Global optimality conditions for quadratic 0-1 optimization problems," Journal of Global Optimization, Springer, vol. 46(2), pages 191-206, February.
    2. Gili Rosenberg & Mohammad Vazifeh & Brad Woods & Eldad Haber, 2016. "Building an iterative heuristic solver for a quantum annealer," Computational Optimization and Applications, Springer, vol. 65(3), pages 845-869, December.
    3. Shivkumar Sabesan & Niranjan Chakravarthy & Kostas Tsakalis & Panos Pardalos & Leon Iasemidis, 2009. "Measuring resetting of brain dynamics at epileptic seizures: application of global optimization and spatial synchronization techniques," Journal of Combinatorial Optimization, Springer, vol. 17(1), pages 74-97, January.
    4. Gary Kochenberger & Jin-Kao Hao & Fred Glover & Mark Lewis & Zhipeng Lü & Haibo Wang & Yang Wang, 2014. "The unconstrained binary quadratic programming problem: a survey," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 58-81, July.
    5. D. Li & X. Sun & C. Liu, 2012. "An exact solution method for unconstrained quadratic 0–1 programming: a geometric approach," Journal of Global Optimization, Springer, vol. 52(4), pages 797-829, April.
    6. Z. Wu & G. Li & J. Quan, 2011. "Global optimality conditions and optimization methods for quadratic integer programming problems," Journal of Global Optimization, Springer, vol. 51(3), pages 549-568, November.
    7. Wanpracha Chaovalitwongse & Oleg Prokopyev & Panos Pardalos, 2006. "Electroencephalogram (EEG) time series classification: Applications in epilepsy," Annals of Operations Research, Springer, vol. 148(1), pages 227-250, November.

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